Improving Data Quality in Traditional Low-Dose Scanning Transmission Electron Microscopy Imaging

It has become very important to study and find optimal conditions for imaging electron-beam (e-beam) sensitive materials in scanning transmission electron microscopy under low electron-dose with high signal-to-noise ratio (SNR). Convergence and collection angles and electron-probe current are essential parameters. However, these parameters have rarely been discussed in a systematic way. In this paper, the illumination and collection conditions are optimized according to the resolution requirement of different materials by adjusting the condenser and intermediate lenses in a commercial transmission electron microscope. To demonstrate the significance of optimizing these parameters, two examples, zeolite MFI and metal–organic framework (MOF) MIL-101, are taken among the sensitive materials, with the most important electron incidences along the [010] and <110> directions, respectively. High SNR atomic resolution images of MFI are obtained with e-beam current as low as 0.50 pA, reaching information transfer for reflection up to 18 0 2 corresponding to d-spacing of 0.11 nm, close to the resolution limit of 0.098 nm from resolvable diffraction limit. MOF MIL-101 is characterized under an even lower e-beam 0.2 pA to avoid severe beam damage. High-quality annular dark and bright field images are obtained, which proves the wide applicability of this method on more e-beam sensitive materials.     

A flexible block classical Gram–Schmidt skeleton with reorthogonalization

We investigate a variant of the reorthogonalized block classical Gram–Schmidt method for computing the QR factorization of a full column rank matrix. Our aim is to bound the loss of orthogonality even when the first local QR algorithm is only conditionally stable. In particular, this allows the use of modified Gram–Schmidt instead of Householder transformations as the first local QR algorithm. Numerical experiments confirm the stable behavior of the new variant. We also examine the use of non-QR local factorization and show by example that the resulting variants, although less stable, may also be applied to ill-conditioned problems.     

Vacuum Rabi Splitting and Kerr Effect of a Hybrid Spin–Magnon–Photon System

The vacuum Rabi splitting and Kerr effect are investigated theoretically in a hybrid spin–magnon–photon system, where the nitrogen-vacancy center in diamond driven by two light fields is coupled to a spherical micromagnet embedded in a superconducting coplanar waveguide resonator. The results indicate that the phenomenon of the Mollow triplet and vacuum Rabi splitting can appear by controlling the spin–magnon coupling and magnon–photon coupling. It is shown that the probe absorption spectrum can be adjusted effectively via the pump frequency detuning. Moreover, it is demonstrated that the optical Kerr effect can be tuned by changing the Rabi frequency. This work may provide a possibility for the applications in quantum information processing and quantum sensing of magnetic signal.     

Tunable Transmissive Metastructure for Precise or Broadband Polarization Conversion Modulation Based on Graphene

Based on the principle of Fabry–Perot (F–P) cavity resonance and the selective permeability of gratings to specific electromagnetic waves, a graphene-based metastructure (MS) is proposed for transmissive polarization conversion (PC). Using the full-wave numerical simulation, it is found that by varying the Fermi energy of graphene, the effective resonance range of the suggested MS can be dynamically adjusted from 0.47 to 0.348–0.714 THz, achieving the target of precise to ultra-broadband polarization modulation. In this paper, the plausibility of the structure is verified from multiple perspectives, and the correlation analyses of the electric and magnetic fields are the supporting illustrations. Additionally, the triggering mechanism of PC is visually illustrated in the study of the surface currents distributions. Simulation results reveal that the MS is superior in performance, functionality, and principle, and it is foreseen to hold excellent promise for integrated equipment in the terahertz (THz) band.     

A generalized Duffing equation with the Coulomb’s friction law and Signorini–type contact conditions

This work provides mathematical and numerical analyses for a spring–mass system, in which Signorini–type contact conditions and Coulomb’s friction law with thermal effects are taken into consideration. The motion of a mass attached to a viscoelastic (Kelvin–Voigt type) nonlinear spring is described by a generalized Duffing equation. Signorini contact conditions are understood as extended complementarity conditions (CCs), where convolution is incorporated, allowing to consider thermal aspects of an obstacle. We prove the existence of global weak solutions for the highly nonlinear differential equation system with all the conditions, based on the regularized differential equation and the normal compliance condition with the standard mollifier. In addition, we investigate what side effects produce higher singularities of contact forces in dynamic contact problems, which is also supported by numerical evidences. Numerical schemes are proposed and then several groups of data are selected for the display of our numerical simulations.     

Dynamics and steady-state analysis of a consumer-resource model

This paper is concerned with the dynamics of a consumer-resource reaction diffusion model in the heterogeneous environment, proposed by Zhang et al. (2017). We use the comparison principle to improve the ultimate bounds step by step, and show that the unique steady state is globally asymptotically stable if the resources are fully limited uniformly in space and consumer population abundance is homogeneous in space.     

Dynamics of a predator–prey system with inducible defense and disease in the prey

Establishing and researching a population dynamical model based on the differential equation is of great significance. In this paper, a predator–prey system with inducible defense and disease in the prey is built from biological evolution and Eco-epidemiology. The effect of disease on population stability in the predator–prey system with inducible defense is studied. Firstly, we verify the positivity and uniform boundedness of the solutions of the system. Then the existence and stability of the equilibria are studied. There are no more than nine equilibrium points in the system. We use a sophisticated parameter transformation to study the properties of the coexistence equilibrium points of the system. A sufficient condition is established for the existence of Hopf bifurcation. Numerical simulations are performed to make analytical studies more complete.     

Gap functions and global error bounds for differential variational–hemivariational inequalities

This paper concerns with the study of a differential variational–hemivariational inequality (DVHVI, for short) in infinite-dimensional Banach spaces. We first introduce the new concept of gap functions for the variational control system of (DVHVI). Then, we consider two kinds of gap functions which are regularized gap function and Moreau–Yosida regularized gap function, respectively, and examine the relevant properties of the gap functions. Moreover, two global error bounds which depend implicitly on the regularized gap function and the Moreau–Yosida regularized gap function, accordingly, are obtained. Finally, in order to illustrate the applicability of the theoretical results, we investigate a coupled dynamic system which is formulated by a nonlinear reaction–diffusion equation described by a time-dependent nonsmooth semipermeability problem.     

Variational methods for fluid–structure interaction and porous media

In this work we consider a poroelastic, flexible material that may deform largely, which is situated in an incompressible fluid driven by the Navier–Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Fréchet-derivative of a non-convex functional as well as (second order in time) inertia terms.     

Global strong solutions to the viscous liquid–gas two-phase flow model with slip boundary conditions in 3D exterior domains

This paper is concerned with the viscous liquid–gas two-phase flow model in a three-dimensional exterior domain with the slip boundary conditions. We are able to prove the existence of a global strong solution when the initial total energy is suitably small. The initial masses of liquid and gas are allowed to contain a vacuum, with no extra restriction between the initial masses of liquid and gas. It should be noted here that we consider the slip boundary condition in a three dimensional (3D) exterior domain which is in sharp contrast to result of Yu (2021) where they consider the Cauchy problem.